Ball bats, particularly composite ball bats, have been designed with various stiffness properties to meet the preferences of various players. Many players, for example, prefer the feel and performance of ball bats having barrels that exhibit high compliance (for example, high radial deflection) and low stiffness. There are challenges, however, in making an effective, durable ball bat having these properties. In addition, there are challenges in making a ball bat with high compliance that can meet league or association rules, such as rules associated with the Bat-Ball Coefficient of Restitution (“BBCOR”), the Batted-Ball Speed (“BBS”) value, or other rules associated with collision efficiency of a bat and a ball.